Question: Simplify the following expression: $\dfrac{72q}{90q^4}$ You can assume $q \neq 0$.
Explanation: $ \dfrac{72q}{90q^4} = \dfrac{72}{90} \cdot \dfrac{q}{q^4} $ To simplify $\frac{72}{90}$ , find the greatest common factor (GCD) of $72$ and $90$ $72 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $90 = 2 \cdot 3 \cdot 3 \cdot 5$ $ \mbox{GCD}(72, 90) = 2 \cdot 3 \cdot 3 = 18 $ $ \dfrac{72}{90} \cdot \dfrac{q}{q^4} = \dfrac{18 \cdot 4}{18 \cdot 5} \cdot \dfrac{q}{q^4} $ $\phantom{ \dfrac{72}{90} \cdot \dfrac{1}{4}} = \dfrac{4}{5} \cdot \dfrac{q}{q^4} $ $ \dfrac{q}{q^4} = \dfrac{q}{q \cdot q \cdot q \cdot q} = \dfrac{1}{q^3} $ $ \dfrac{4}{5} \cdot \dfrac{1}{q^3} = \dfrac{4}{5q^3} $